Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin-population imbalance. Up to the third order, we calculate the high-temperature free energy of a unitary Fermi gas as a function of spin imbalance, with infinitely large attractive or repulsive interactions. In the latter repulsive case, we show that there is no itinerant ferromagnetism when quantum virial expansion is applicable. We therefore estimate an upper bound for the ferromagnetic transition temperature ${T}_{c}$ . For a harmonically trapped Fermi gas at unitarity, we find that $({T}_{c}){}_{\mathrm{upper}}<{T}_{F}$ , where ${T}_{F}$ is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin-population imbalance. Up to the third order, we calculate the high-temperature free energy of a unitary Fermi gas as a function of spin imbalance, with infinitely large attractive or repulsive interactions. In the latter repulsive case, we show that there is no itinerant ferromagnetism when quantum virial expansion is applicable. We therefore estimate an upper bound for the ferromagnetic transition temperature ${T}_{c}$. For a harmonically trapped Fermi gas at unitarity, we find that $({T}_{c}){}_{\mathrm{upper}}<{T}_{F}$, where ${T}_{F}$ is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.

arXiv:1008.1457Physical Review AOct 26, 201028 citations

Strongly-interacting Fermi gases with population imbalance

Mark Ku

This thesis presents a theoretical study of strongly-interacting Fermi systems with population imbalance, which is motivated by some differences in cold atoms experiments. We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different species fermions in anisotropic traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization, the limit of resonance superfluidity in traps. Our findings contribute to understanding some experimental discrepancies as finite-size and confinement effects. For an imbalanced gas in the uniform system, we calculate the energy of adding an impurity, and construct the equation of state of the partially-polarized normal Fermi liquid. Finally, we study the properties of a spin-down polaron in a trapped gas containing arbitrary numbers of spin-up and spin-down fermions, and derive a self-consistent equation for the polaron energy.This thesis presents a theoretical study of strongly-interacting Fermi systems with population imbalance, which is motivated by some differences in cold atoms experiments. We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different species fermions in anisotropic traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization, the limit of resonance superfluidity in traps. Our findings contribute to understanding some experimental discrepancies as finite-size and confinement effects. For an imbalanced gas in the uniform system, we calculate the energy of adding an impurity, and construct the equation of state of the partially-polarized normal Fermi liquid. Finally, we study the properties of a spin-down polaron in a trapped gas containing arbitrary numbers of spin-up and spin-down fermions, and derive a self-consistent equation for the polaron energy.

Jan 1, 20090 citations

Phase Diagram of A One Dimensional Spin-Imbalanced Fermi Gas

Ann Sophie C. Rittner, Yean-an Liao, Tobias Paprotta +3 more

Bulletin of the American Physical SocietyMay 23, 20090 citations

Dimensional crossover in a spin-imbalanced Fermi gas

Shovan Dutta, Erich J. Mueller

We model the one-dimensional (1D) to three-dimensional (3D) crossover in a cylindrically trapped Fermi gas with attractive interactions and spin imbalance. We calculate the mean-field phase diagram and study the relative stability of exotic superfluid phases as a function of interaction strength and temperature. For weak interactions and low density, we find 1D-like behavior, which repeats as a function of the chemical potential as new channels open. For strong interactions, mixing of single-particle levels gives 3D-like behavior at all densities. Furthermore, we map the system to an effective 1D model, finding significant density dependence of the effective 1D scattering length.We model the one-dimensional (1D) to three-dimensional (3D) crossover in a cylindrically trapped Fermi gas with attractive interactions and spin imbalance. We calculate the mean-field phase diagram and study the relative stability of exotic superfluid phases as a function of interaction strength and temperature. For weak interactions and low density, we find 1D-like behavior, which repeats as a function of the chemical potential as new channels open. For strong interactions, mixing of single-particle levels gives 3D-like behavior at all densities. Furthermore, we map the system to an effective 1D model, finding significant density dependence of the effective 1D scattering length.

arXiv:1508.03352Physical Review ADec 21, 201612 citations

{T}_{c}

. For a harmonically trapped Fermi gas at unitarity, we find that

({T}_{c}){}_{\mathrm{upper}}<{T}_{F}

, where

{T}_{F}

is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.